Номер 7, страница 133 - гдз по физике 9 класс учебник Шахмаев, Бунчук

Физика, 9 класс Учебник, авторы: Шахмаев Николай Михайлович, Бунчук Алексей Васильевич, издательство Мнемозина, Москва, 2007, голубого цвета

Авторы: Шахмаев Н. М., Бунчук А. В.

Тип: Учебник

Издательство: Мнемозина

Год издания: 2007 - 2026

Цвет обложки: голубой

ISBN: 978-5-346-01799-8

Глава 8. Закон сохранения энергии. Параграф 30. Закон сохранения механической энергии - номер 7, страница 133.

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            "text" => "<p><strong>7.</strong> Автомобиль массой 2 т затормозил и остановился, пройдя путь 50 м. Определите работу силы трения и изменение кинетической энергии автомобиля, если дорога горизонтальна, а коэффициент трения равен 0,4.</p>"
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            "text" => "<p><strong>Дано:</strong></p><p>$m = 2 \text{ т} = 2000 \text{ кг}$</p><p>$s = 50 \text{ м}$</p><p>$\mu = 0,4$</p><p>$g \approx 10 \text{ м/с²}$</p><p>Автомобиль остановился, следовательно, его конечная скорость $v_к = 0 \text{ м/с}$.</p><p><strong>Найти:</strong></p><p>$A_{тр}$ — работа силы трения</p><p>$\Delta E_k$ — изменение кинетической энергии</p><p><strong>Решение:</strong></p><p><strong>Работа силы трения</strong></p><p>Работа силы определяется формулой $A = F \cdot s \cdot \cos\alpha$, где $\text{F}$ — модуль силы, $\text{s}$ — модуль перемещения, а $\alpha$ — угол между вектором силы и вектором перемещения.</p><p>Сила трения скольжения $F_{тр}$ всегда направлена против движения. Следовательно, угол $\alpha$ между вектором силы трения и вектором перемещения равен $180^\circ$, а $\cos(180^\circ) = -1$.</p><p>Таким образом, работа силы трения вычисляется как $A_{тр} = -F_{тр} \cdot s$.</p><p>Поскольку дорога горизонтальна, сила нормальной реакции опоры $\text{N}$ равна по модулю силе тяжести $mg$: $N = mg$.</p><p>Силу трения найдем по формуле $F_{тр} = \mu N = \mu mg$.</p><p>Подставим числовые значения:</p><p>$F_{тр} = 0,4 \cdot 2000 \text{ кг} \cdot 10 \text{ м/с²} = 8000 \text{ Н}$.</p><p>Теперь можем рассчитать работу силы трения:</p><p>$A_{тр} = -8000 \text{ Н} \cdot 50 \text{ м} = -400000 \text{ Дж} = -400 \text{ кДж}$.</p><p><strong>Ответ:</strong> работа силы трения равна $-400 \text{ кДж}$.</p><p><strong>Изменение кинетической энергии</strong></p><p>Согласно теореме о кинетической энергии, изменение кинетической энергии тела равно работе всех сил, действующих на него: $\Delta E_k = A_{нет}$.</p><p>При торможении на горизонтальной дороге на автомобиль действуют: сила тяжести, сила нормальной реакции опоры и сила трения. Сила тяжести и сила реакции опоры перпендикулярны направлению движения и, следовательно, работы не совершают. Работа двигателя равна нулю, так как автомобиль тормозит.</p><p>Таким образом, полная работа, совершённая над автомобилем, равна работе силы трения: $A_{нет} = A_{тр}$.</p><p>Следовательно, изменение кинетической энергии автомобиля равно работе силы трения, которую мы уже нашли:</p><p>$\Delta E_k = A_{тр} = -400 \text{ кДж}$.</p><p><strong>Ответ:</strong> изменение кинетической энергии автомобиля равно $-400 \text{ кДж}$.</p>"
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            "id" => 1732402
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            "task" => array:2 [
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            "text" => "<p><strong>Дано:</strong></p><p>$m = 2 \text{ т} = 2000 \text{ кг}$</p><p>$s = 50 \text{ м}$</p><p>$\mu = 0,4$</p><p>$g \approx 10 \text{ м/с²}$</p><p>Автомобиль остановился, следовательно, его конечная скорость $v_к = 0 \text{ м/с}$.</p><p><strong>Найти:</strong></p><p>$A_{тр}$ — работа силы трения</p><p>$\Delta E_k$ — изменение кинетической энергии</p><p><strong>Решение:</strong></p><p><strong>Работа силы трения</strong></p><p>Работа силы определяется формулой $A = F \cdot s \cdot \cos\alpha$, где $\text{F}$ — модуль силы, $\text{s}$ — модуль перемещения, а $\alpha$ — угол между вектором силы и вектором перемещения.</p><p>Сила трения скольжения $F_{тр}$ всегда направлена против движения. Следовательно, угол $\alpha$ между вектором силы трения и вектором перемещения равен $180^\circ$, а $\cos(180^\circ) = -1$.</p><p>Таким образом, работа силы трения вычисляется как $A_{тр} = -F_{тр} \cdot s$.</p><p>Поскольку дорога горизонтальна, сила нормальной реакции опоры $\text{N}$ равна по модулю силе тяжести $mg$: $N = mg$.</p><p>Силу трения найдем по формуле $F_{тр} = \mu N = \mu mg$.</p><p>Подставим числовые значения:</p><p>$F_{тр} = 0,4 \cdot 2000 \text{ кг} \cdot 10 \text{ м/с²} = 8000 \text{ Н}$.</p><p>Теперь можем рассчитать работу силы трения:</p><p>$A_{тр} = -8000 \text{ Н} \cdot 50 \text{ м} = -400000 \text{ Дж} = -400 \text{ кДж}$.</p><p><strong>Ответ:</strong> работа силы трения равна $-400 \text{ кДж}$.</p><p><strong>Изменение кинетической энергии</strong></p><p>Согласно теореме о кинетической энергии, изменение кинетической энергии тела равно работе всех сил, действующих на него: $\Delta E_k = A_{нет}$.</p><p>При торможении на горизонтальной дороге на автомобиль действуют: сила тяжести, сила нормальной реакции опоры и сила трения. Сила тяжести и сила реакции опоры перпендикулярны направлению движения и, следовательно, работы не совершают. Работа двигателя равна нулю, так как автомобиль тормозит.</p><p>Таким образом, полная работа, совершённая над автомобилем, равна работе силы трения: $A_{нет} = A_{тр}$.</p><p>Следовательно, изменение кинетической энергии автомобиля равно работе силы трения, которую мы уже нашли:</p><p>$\Delta E_k = A_{тр} = -400 \text{ кДж}$.</p><p><strong>Ответ:</strong> изменение кинетической энергии автомобиля равно $-400 \text{ кДж}$.</p>"
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          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "next" => array:2 [
      "refs" => "1437061"
      "type" => "task"
    ]
    "previous" => array:2 [
      "refs" => "1437059"
      "type" => "task"
    ]
    "book" => Illuminate\Database\Eloquent\Collection {#1149
      #items: array:1 [
        0 => App\Models\Book {#1150
          #connection: "mysql"
          #table: "books"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: false
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:50 [
            "id" => 2906
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_tree_default_status" => "tasks"
            "field_pages_status" => null
            "field_subject" => Illuminate\Database\Eloquent\Collection {#1151
              #items: array:1 [
                0 => App\Models\Term {#1152
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:10 [
                    "id" => 6493
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Физика"
                    "field_abbreviated_name" => null
                    "field_cases" => array:6 [ …6]
                    "field_foreign_lang_name" => null
                    "field_short_name" => null
                    "field_subject_type" => "technical_subject"
                    "field_translit" => "fizika"
                  ]
                  #original: array:10 [
                    "id" => 6493
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Физика"
                    "field_abbreviated_name" => null
                    "field_cases" => array:6 [ …6]
                    "field_foreign_lang_name" => null
                    "field_short_name" => null
                    "field_subject_type" => "technical_subject"
                    "field_translit" => "fizika"
                  ]
                  #changes: []
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                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
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                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_class" => Illuminate\Database\Eloquent\Collection {#1153
              #items: array:1 [
                0 => App\Models\Term {#1154
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 5458
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "9"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "devjatyj"
                  ]
                  #original: array:6 [
                    "id" => 5458
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "9"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "devjatyj"
                  ]
                  #changes: []
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                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_publisher" => Illuminate\Database\Eloquent\Collection {#1155
              #items: array:1 [
                0 => App\Models\Term {#1156
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 5155
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Мнемозина"
                    "field_cases" => null
                    "field_translit" => "mnemozina"
                  ]
                  #original: array:6 [
                    "id" => 5155
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Мнемозина"
                    "field_cases" => null
                    "field_translit" => "mnemozina"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_author" => Illuminate\Database\Eloquent\Collection {#1157
              #items: array:2 [
                0 => App\Models\Term {#1158
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:12 [
                    "id" => 6294
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Шахмаев"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Николай"
                    "field_patronymic" => "Михайлович"
                    "field_surname_rp" => null
                  ]
                  #original: array:12 [
                    "id" => 6294
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Шахмаев"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Николай"
                    "field_patronymic" => "Михайлович"
                    "field_surname_rp" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                1 => App\Models\Term {#1159
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:12 [
                    "id" => 3942
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Бунчук"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Алексей"
                    "field_patronymic" => "Васильевич"
                    "field_surname_rp" => null
                  ]
                  #original: array:12 [
                    "id" => 3942
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Бунчук"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Алексей"
                    "field_patronymic" => "Васильевич"
                    "field_surname_rp" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1160
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_book_type" => Illuminate\Database\Eloquent\Collection {#1161
              #items: array:1 [
                0 => App\Models\Term {#1162
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:10 [
                    "id" => 6671
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Учебник"
                    "field_book_type_foreign" => null
                    "field_cases" => array:6 [ …6]
                    "field_plural_form" => null
                    "field_short_name" => null
                    "field_short_name_foreign" => null
                    "field_translit" => "uchebnik"
                  ]
                  #original: array:10 [
                    "id" => 6671
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Учебник"
                    "field_book_type_foreign" => null
                    "field_cases" => array:6 [ …6]
                    "field_plural_form" => null
                    "field_short_name" => null
                    "field_short_name_foreign" => null
                    "field_translit" => "uchebnik"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_country" => Illuminate\Database\Eloquent\Collection {#1163
              #items: array:1 [
                0 => App\Models\Term {#1164
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 9
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Россия"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "rossiya"
                  ]
                  #original: array:6 [
                    "id" => 9
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Россия"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "rossiya"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_city" => Illuminate\Database\Eloquent\Collection {#1165
              #items: array:1 [
                0 => App\Models\Term {#1166
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 15
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Москва"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "moskva"
                  ]
                  #original: array:6 [
                    "id" => 15
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Москва"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "moskva"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_series" => Illuminate\Database\Eloquent\Collection {#1167
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_umk" => Illuminate\Database\Eloquent\Collection {#1168
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1169
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1170
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_publication_number" => "4"
            "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1171
              #items: array:1 [
                0 => App\Models\Term {#1172
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 33
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "стереотипное"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "stereotipnoe"
                  ]
                  #original: array:6 [
                    "id" => 33
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "стереотипное"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "stereotipnoe"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1173
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_under_the_edition_degree" => null
            "field_cover_description" => null
            "field_publication_year" => "2007"
            "field_publication_year_until" => null
            "field_part" => ""
            "field_part_writing" => ""
            "field_second_foreign_language" => null
            "field_for_whom" => "Учебное издание"
            "field_allowed" => null
            "field_reserve_field" => null
            "field_link_to_source" => null
            "field_tasks_count" => "362"
            "field_priority" => null
            "field_default_folder" => "/fizika_09/shahmaev-u/"
            "field_isbn" => "978-5-346-01799-8"
            "field_cover" => array:1 [
              0 => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267"
            ]
            "field_cover_alts" => array:1 [
              0 => ""
            ]
            "field_covers" => array:1 [
              0 => array:4 [
                "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267"
                "alt" => ""
                "width" => "2294"
                "height" => "3039"
              ]
            ]
            "field_popular_book" => "0"
            "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1174
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_new_book" => Illuminate\Database\Eloquent\Collection {#1175
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_old_book" => Illuminate\Database\Eloquent\Collection {#1176
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_url" => "/9-klass/fizika/shahmaev-uchebnik"
            "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1177
              #items: array:1 [
                0 => App\Models\Term {#1178
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 52
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "голубой"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "goluboy"
                  ]
                  #original: array:6 [
                    "id" => 52
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "голубой"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "goluboy"
                  ]
                  #changes: []
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                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
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                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
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                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "breadcrumbs" => array:3 [
              "class" => 380
              "subject" => 556
              "class_subject" => 493
            ]
          ]
          #original: array:50 [
            "id" => 2906
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_tree_default_status" => "tasks"
            "field_pages_status" => null
            "field_subject" => Illuminate\Database\Eloquent\Collection {#1151}
            "field_class" => Illuminate\Database\Eloquent\Collection {#1153}
            "field_publisher" => Illuminate\Database\Eloquent\Collection {#1155}
            "field_author" => Illuminate\Database\Eloquent\Collection {#1157}
            "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1160}
            "field_book_type" => Illuminate\Database\Eloquent\Collection {#1161}
            "field_country" => Illuminate\Database\Eloquent\Collection {#1163}
            "field_city" => Illuminate\Database\Eloquent\Collection {#1165}
            "field_series" => Illuminate\Database\Eloquent\Collection {#1167}
            "field_umk" => Illuminate\Database\Eloquent\Collection {#1168}
            "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1169}
            "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1170}
            "field_publication_number" => "4"
            "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1171}
            "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1173}
            "field_under_the_edition_degree" => null
            "field_cover_description" => null
            "field_publication_year" => "2007"
            "field_publication_year_until" => null
            "field_part" => ""
            "field_part_writing" => ""
            "field_second_foreign_language" => null
            "field_for_whom" => "Учебное издание"
            "field_allowed" => null
            "field_reserve_field" => null
            "field_link_to_source" => null
            "field_tasks_count" => "362"
            "field_priority" => null
            "field_default_folder" => "/fizika_09/shahmaev-u/"
            "field_isbn" => "978-5-346-01799-8"
            "field_cover" => array:1 [
              0 => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267"
            ]
            "field_cover_alts" => array:1 [
              0 => ""
            ]
            "field_covers" => array:1 [
              0 => array:4 [
                "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267"
                "alt" => ""
                "width" => "2294"
                "height" => "3039"
              ]
            ]
            "field_popular_book" => "0"
            "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1174}
            "field_new_book" => Illuminate\Database\Eloquent\Collection {#1175}
            "field_old_book" => Illuminate\Database\Eloquent\Collection {#1176}
            "field_url" => "/9-klass/fizika/shahmaev-uchebnik"
            "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1177}
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    "page" => Illuminate\Database\Eloquent\Collection {#1485
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                2 => App\Models\Task {#1392
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                3 => App\Models\Task {#1403
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№7 (с. 133)
Условие. №7 (с. 133)
скриншот условия
Физика, 9 класс Учебник, авторы: Шахмаев Николай Михайлович, Бунчук Алексей Васильевич, издательство Мнемозина, Москва, 2007, голубого цвета, страница 133, номер 7, Условие

7. Автомобиль массой 2 т затормозил и остановился, пройдя путь 50 м. Определите работу силы трения и изменение кинетической энергии автомобиля, если дорога горизонтальна, а коэффициент трения равен 0,4.

Решение. №7 (с. 133)

Дано:

$m = 2 \text{ т} = 2000 \text{ кг}$

$s = 50 \text{ м}$

$\mu = 0,4$

$g \approx 10 \text{ м/с²}$

Автомобиль остановился, следовательно, его конечная скорость $v_к = 0 \text{ м/с}$.

Найти:

$A_{тр}$ — работа силы трения

$\Delta E_k$ — изменение кинетической энергии

Решение:

Работа силы трения

Работа силы определяется формулой $A = F \cdot s \cdot \cos\alpha$, где $\text{F}$ — модуль силы, $\text{s}$ — модуль перемещения, а $\alpha$ — угол между вектором силы и вектором перемещения.

Сила трения скольжения $F_{тр}$ всегда направлена против движения. Следовательно, угол $\alpha$ между вектором силы трения и вектором перемещения равен $180^\circ$, а $\cos(180^\circ) = -1$.

Таким образом, работа силы трения вычисляется как $A_{тр} = -F_{тр} \cdot s$.

Поскольку дорога горизонтальна, сила нормальной реакции опоры $\text{N}$ равна по модулю силе тяжести $mg$: $N = mg$.

Силу трения найдем по формуле $F_{тр} = \mu N = \mu mg$.

Подставим числовые значения:

$F_{тр} = 0,4 \cdot 2000 \text{ кг} \cdot 10 \text{ м/с²} = 8000 \text{ Н}$.

Теперь можем рассчитать работу силы трения:

$A_{тр} = -8000 \text{ Н} \cdot 50 \text{ м} = -400000 \text{ Дж} = -400 \text{ кДж}$.

Ответ: работа силы трения равна $-400 \text{ кДж}$.

Изменение кинетической энергии

Согласно теореме о кинетической энергии, изменение кинетической энергии тела равно работе всех сил, действующих на него: $\Delta E_k = A_{нет}$.

При торможении на горизонтальной дороге на автомобиль действуют: сила тяжести, сила нормальной реакции опоры и сила трения. Сила тяжести и сила реакции опоры перпендикулярны направлению движения и, следовательно, работы не совершают. Работа двигателя равна нулю, так как автомобиль тормозит.

Таким образом, полная работа, совершённая над автомобилем, равна работе силы трения: $A_{нет} = A_{тр}$.

Следовательно, изменение кинетической энергии автомобиля равно работе силы трения, которую мы уже нашли:

$\Delta E_k = A_{тр} = -400 \text{ кДж}$.

Ответ: изменение кинетической энергии автомобиля равно $-400 \text{ кДж}$.

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